縱-扭模態耦合之三角形超音波馬達

Longitudinal – Torsional Mode Coupled Triangular Ultrasonic Motors

郇心慧(Hsin-Hui Hsun)

指導教授 ： 尹慶中

國立交通大學/工學院/機械工程系所/碩士(2013年)

https://doi.org/10.6842/NCTU.2013.00637

摘要

本研究改良蔡慶芳學長設計之三角形超音波馬達，希望以不同方形
壓電片分別致振縱向模態與扭轉模態來驅動馬達，三角形馬達定子的三
頂點設為與轉子之接觸點，並在頂角接近底座處切割橫向孔縫，減損定
子的軸向剛性。定子的三個側面各黏貼三片方形壓電陶瓷材料，施予電
極固定相位差之交流電壓，以相同工作頻率、振幅激發定子的縱向與扭
轉共振模態。兩共振模態的耦合振動致使定子接觸點作橢圓軌跡運動，
定子與轉子間存在的摩擦力致使轉子轉動。調整輸入電壓的相位差，可
控制轉子轉動方向。本文採用有限元素分析軟體進行數值模擬，以三角
形定子水平孔縫長度與位置為主要設計參數，依據模態耦合與模態隔離
程度，找出可同時激發縱向與扭轉模態的幾何模型，分析馬達定子作動
時接觸點的運動軌跡。超音波馬達原型機的定子材質為鋁合金，轉子為
不銹鋼，進行馬達性能曲線測試，最大轉速為59rpm，最大扭矩為
2.91N-cm。

關鍵字

超音波馬達 ； 雙模態共振 ； 扭矩轉速曲線

並列摘要

This thesis presents an improvement of the triangular ultrasonic
originally designed by Tsai. The longitudinal mode and torsional mode of the
stator are excited to drive the rotor by distinct rectangular elements of PZT-4.
The stator looks like a triangular tube machined with three horizontal slots in
the apexes, which are set as contact points. The short tube is used to have a
higher natural frequency for longitudinal mode than the torsional mode. Both
longitudinal mode and torsional mode can have the same natural frequency if
the axial stiffness is degraded by the horizontal slots. The PZT-4 element with
segmented electrodes is adhered to each peripheral surface of the stator. The
AC signals with constant phase difference are applied to the electrodes to
excite both vibration modes. Every contact point experiences an elliptical
trajectory in response to a harmonic excitation of the coupled modes, which
are used to propel the ultrasonic motor through frictional force between the
rotor and stator. The revolution direction of the rotor can be controlled by
adjusting the phase difference of input signals. A finite element analysis code
is used to calculate the resonant frequencies of the stator with various design
iii
parameters, including the length and position of the horizontal slots in the
stator. In the probably optimal trial, both longitudinal and torsional modes can
be simultaneously excited in a numerical model of the stator at the same
frequency in accordance with modal separation and dual mode coupling
theory. The trajectory of a contact point between the stator and rotor has been
analyzed. The prototypes of the presented ultrasonic motors were fabricated
and tested. The stator and rotor are made of aluminum alloy and stainless steel,
respectively. The maximum measured revolution speed is 59 rpm without
payload, and the maximum measured torque is 2.91 N-cm.

並列關鍵字

Ultrasonic motor ； dual-mode resonance ； torque-revolution curve

參考文獻

[14] 蔡慶芳 （2011）, 雙模態耦合的三角形超音波馬達, 國立交通大學

[20] 游泰和 （2012）, 圓柱楔形超音波馬達之研發, 國立交通大學機械

“Equivalent circuits of piezoelectric motor,” Bulletin of Kiev

UK Patent Application GB2020857（A）.

[5] T. Sashida and T. Kenjo （1993）, An Introduction to Ultrasonic Motors,